Principal Magistrate Vishal Singh granted bail to the boy, who has just turned major, on furnishing a bond of Rs 50,000.
The board had earlier denied bail to the juvenile twice by observing that he was a repeat offender and had blamed his parents for allowing him to drive at such an age.
The boy sought bail saying he has given his 12th standard exams and has to appear in various entrance examinations and that he was depressed as he was away from his family.
Advocate Vikas Manchanda, who appeared for the youth, submitted that the future prospects of the child were involved here and if he is not allowed to give competitive exams, it can ruin his career.
He said that the boy has already missed several exams during his stay in the reform home and he should be granted bail to enable him to appear in the rest of the examinations.
The board had earlier asked the counsel to furnish the admit cards and other documents relating to the exams which were given to the JJB.
The bail plea, however, was opposed by the police and prosecutor Atul Shrivastava sought to see the psychology reports of the boy.
While rejecting the boy's earlier bail pleas, the board had observed that repeated traffic rule violation challans failed to have any "reformative effect" upon the juvenile and it seemed his parents did not care.
The incident took place on April 4 when marketing executive Siddharth Sharma was trying to cross a road near Ludlow Castle school and the speeding Mercedes hit him.
A case under IPC sections 304 A (causing death by rash or negligent act), 279 (driving on a public way so rashly or negligently as to endanger human life) and 337 (causing hurt by an act which endangers human life) was lodged against him.
Mercedes hit-and-run: Father of teen driving car arrested
Mercedes hit-and-run: Teen's bail rejected, 'bad parenting' blamed
Mercedes hit-and-run: Teenage accused to be questioned
One critical after BMW hits four in Noida, driver flees
Cop tries to stop speeding car, dragged for 300 metres